Soft Maximal and Irreducible Int-Ideals of a Ring
18 Mar 2020-New Mathematics and Natural Computation (World Scientific Publishing Company)-Vol. 16, Iss: 01, pp 37-52
TL;DR: The concepts of soft maximal int-ideal and soft irreducible int-Ideal of a ring are introduced and some properties of these notions have been studied.
Abstract: In this paper, the concepts of soft maximal int-ideal and soft irreducible int-ideal of a ring are introduced and some properties of these notions have been studied. Also we point out some facts of...
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TL;DR: It is shown that the concepts of soft elementwise ring and soft int-ring of a ring are equivalent and the notions of minimal generating set for a soft int -ideal and soft principal int-ideal are presented.
Abstract: In this paper, the notion of soft elementwise ring is introduced and it is shown that the concepts of soft elementwise ring and soft int-ring of a ring are equivalent. The concept of soft direct su...
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TL;DR: In this paper, the concept of fuzzy soft group is introduced and in the meantime, some of their properties and structural characteristics are discussed and studied, including fuzzy soft function and fuzzy soft homomorphism.
Abstract: In this paper, the concept of fuzzy soft group is introduced and in the meantime, some of their properties and structural characteristics are discussed and studied. Furthermore, definitions of fuzzy soft function and fuzzy soft homomorphism are defined and the theorems of homomorphic image and homomorphic pre-image are given. After that, the definition of normal fuzzy soft group is given and some of its basic properties are studied.
261 citations
TL;DR: This paper introduces and study soft subrings and soft ideals of a ring by using Molodtsov's definition of the soft sets, and introduces soft subfields of a field and soft submodule of a left R-module.
Abstract: Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, we introduce and study soft subrings and soft ideals of a ring by using Molodtsov's definition of the soft sets. Moreover, we introduce soft subfields of a field and soft submodule of a left R-module. Some related properties about soft substructures of rings, fields and modules are investigated and illustrated by many examples.
134 citations
17 May 2008
TL;DR: The definition ofsoft modules is presented and some basic properties using modules and Molodtsov's definition of soft sets are constructed.
Abstract: Molodtsov introduced the concept of soft sets.Recently, Aktas et al. generalized soft sets by defining the concept of soft groups. In this paper, we present the definition of soft modules and construct some basic properties using modules and Molodtsov's definition of soft sets.
109 citations
TL;DR: In this paper, a soft intersection group (soft int-group) on a soft set is defined, which functions as a bridge between soft set theory, set theory and group theory and shows the effect of soft sets on a group structure.
Abstract: In this paper, we define a soft intersection group (soft int-group) on a soft set. This new concept functions as a bridge among soft set theory, set theory and group theory and shows the effect of soft sets on a group structure in the sense of intersection and inclusion of sets. We then derive the basic properties of soft int-groups and give its applications to group theory.
84 citations
TL;DR: A new kind of soft ring called soft int-ring is introduced and its various related properties are derived and its structural characteristics are studied.
Abstract: In this paper, we introduce a new kind of soft ring called soft int-ring and derive its various related properties. We then study and discuss its structural characteristics.
25 citations